Fibonacci

Time Limit: 2000 ms Memory Limit: 131072 KiB

Problem Description

Fibonacci numbers are well-known as follow:

 

Now given an integer N, please find out whether N can be represented as the sum of several Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.

Input

Multiple test cases, the first line is an integer T (T<=10000), indicating the number of test cases.

Each test case is a line with an integer N (1<=N<=10^9).

Output

One line per case. If the answer don’t exist, output “-1” (without quotes). Otherwise, your answer should be formatted as “N=f1+f2+…+fn”. N indicates the given number and f1, f2, … , fn indicating the Fibonacci numbers in ascending order. If there are multiple ways, you can output any of them.

 

Sample Input

4
5
6
7
100

Sample Output

5=5
6=1+5
7=2+5
100=3+8+89

Hint

Source

“浪潮杯”山东省第七届ACM大学生程序设计竞赛